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    Area of Science:

    • Optics and Photonics
    • Spectroscopy
    • Interferometry

    Background:

    • Fabry-Perot interferometers are crucial for high-resolution spectroscopy.
    • Accurate spectrum calculation is often hindered by errors in optical path difference and material dispersion.
    • Existing methods may not fully mitigate these reconstruction challenges.

    Purpose of the Study:

    • To present a novel method for calculating incident light spectra from detector signals in a cascaded Fabry-Perot interferometric spectrometer.
    • To address and reduce spectrum reconstruction errors.
    • To improve the accuracy of spectral analysis in interferometric systems.

    Main Methods:

    • Modification of the standard Fabry-Perot integral equation.
    • Development and testing of a transformation algorithm incorporating a modified kernel.
    • Comparison of the new algorithm against the conventional kernel approach.

    Main Results:

    • The developed method effectively reduces spectrum reconstruction errors.
    • Spectral error reductions exceeding 20 dB were achieved compared to the conventional kernel.
    • The algorithm demonstrates improved accuracy in spectral calculations.

    Conclusions:

    • The modified Fabry-Perot integral equation and transformation algorithm offer a significant improvement for spectral calculations.
    • This method provides a more accurate way to determine light spectra, overcoming limitations of previous techniques.
    • The enhanced accuracy has implications for various applications requiring precise spectral analysis.